# Multi-Robot Control Using Time-Varying Density Functions

arXiv: https://arxiv.org/abs/1404.0338 · HTML: https://mlsanity.com/paper/1404.0338/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2014.

## Built on by (most cited first, 3 of 3)

- [Multi-UAV Planning for Cooperative Wildfire Coverage and Tracking with Quality-of-Service Guarantees](https://mlsanity.com/paper/2206.10544/) (2022)
- [LPAC: Learnable Perception-Action-Communication Loops with Applications to Coverage Control](https://mlsanity.com/paper/2401.04855/) (2024)
- [Physics-informed sensor coverage through structure preserving machine learning](https://mlsanity.com/paper/2509.10363/) (2025)

## Abstract (arXiv)

This paper presents an approach to externally influencing a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. To this end, a continuous-time algorithm is proposed that moves the robots so as to provide optimal coverage given the density functions as they evolve over time. The developed algorithm represents an extension to previous coverage algorithms in that time-varying densities are explicitly taken into account in a provable manner. A distributed approximation to this algorithm is moreover proposed whereby the robots only need to access information from adjacent robots. Simulations and robotic experiments show that the proposed algorithms do indeed exhibit the desired behaviors in practice as well as in theory.